This material is provided as a public service to support the student Space Settlement Contest. The views expressed herein are not necessarily those of NASA or any other government body.
L5: An orbit about L5, stable in the four-body problem of the sun, earth, moon and colony, has been shown by Kamel and earlier authors. Cf. references in PTA (ref 2). Occultation of the sun in that orbit is rare and brief. L4 is equally usable.
High-orbit products: The possibility of returning material products to the earth's surface from L5 is not considered in this document.
Authors: Tsiolkowsky in Russia, Bernal in England, and Cole in the U.S.A. all wrote books which bear on the concept of space colonies. Clarke, Stroud and others have also considered portions of the problem.
The image of the sun's disc would rotate about its center, but the disc is so nearly circular that this rotation would not be detectable by the naked eye.
Civil engineering limits: A standard safety factor of 1.67 is used, as in the building industry on earth. (Corresponding factors are 1.5 for commercial aircraft, and as low as 1.2 for military aircraft.) For aluminum/silicon alloy, cold-drawn, with an ultimate strength of 60,000 psi, the yield point is 50,000 psi and the working stress is here taken as 30,000 psi. For hot-formed aluminum, 20,000 psi is used. The same safety factor is used for iron and titanium. Diameters up to four miles are assumed, with total atmospheric pressure of 5 psi minimum. See PTA for formulas. (Mass table in PTA for model 1 has a non-propagating error: for 20,000 tons aluminum read 80,000 tons metals.)
Axis of rotating habitat contains avenue-passage and passes through a hollow bearing. Bearing forces are small, typically one ten-millionth of colony weight in one gravity.
M.I.T. Studies: Cf. references in PTA. Asteroidal materials: Total volume of proven asteroids is estimated as 1/2500 of volume of the earth (Cf. Allan, Astrophysical Constants). Economic imperative is construction of a new colony adjacent to an asteroid, so that economic productivity can be achieved without prior moving of materials. Relocation of a colony to L5 from the asteroidal region would require about 30 years at an expenditure of 7% of total colony mass.
The energy intensity (insolation) in space is 1.4 Kw/m2, or 1.23 x 108 KWH/year for a 100 meter square. This would cost $1.8 x 106 at a busbar rate of 15 mils. The lower figure used in the text allows for reflection losses. Mirror assumed is .001 inches aluminum, with a factor three multiplier for support frames. For an initial community of 10,000 persons, an electrical power plant of 100 megawatts is assumed (10 Kw/person). For the USA in 1975, average usage of electrical energy is at the rate of about 2 Kw/person, and peak capacity is equivalent to 2.5 Kw/person.
The velocity intervals from low earth orbit to lunar parking orbit (LPO), to L5 or to geosynchronous orbit (GSO) are all approximately equal, in the range 11.1 - 11.4 Km/sec for minimum-energy two impulse burns. Escape velocity from the moon is 2.4 Km/sec. With kinetic energy = 1/2 mv2 escape from the earth therefore requires 21.4 times as much energy as from the moon. Spiral orbits (low thrust) require more energy.
The mass driver: A description and table of parameters for this machine is listed in PTA. Further study results will be available in references 4 and 6. Magnetic fields are held below 10,000 gauss, and accelerations to less than 29 gravities. The nominal repetition rate is 1 Hz, for payloads of 9 Kg each. The peak transfer rate is therefore 780 metric tons per day. The range of a factor 4 quoted in the text allows for turnoff during the lunar night, and for reliability down to 50%.
Guidance is by magnetic trimming during a one-kilometer inertial drift-space, roll/pitch/yaw and position sensing being done by laser interferometry before payload release.
In PTA an estimate of 10,000 tons for lift-needs from earth to L5 was given, and 3,000 tons for transfer from the earth to the moon, based on a "Spartan" approach: oxygen atmosphere, construction work force stay time until completion of the first community, and food supply in dehydrated form. Another extreme was given by NASA/ MSFC, based on a nitrogen-mix atmosphere, extensive atmospheric make-up from earth, frequent crew rotation and food resupply in wet form. It was about a factor three higher (unpublished internal report, no number). The extremes are therefore 2% - 6% of an estimated 500,000 ton total mass.
In current discussions of vehicle-systems, a distinction is drawn between lift vehicles made of building-blocks each of which is already under development for the space shuttle (e.g., SRB's, SSME's, avionics) and lift vehicles requiring extensive new development. For the space-colonization program only the former are required. Several papers in ref. 5 (Tischler, Davis, Salkeld) cover this topic.
Construction station: PTA estimate was 1000 tons. A more detailed estimate (G. Driggers, ref. 5) gives 2500 tons.
The source for Table 1 is ref.7. Samples from other ApoUo landing sites have generally greater amounts of aluminum and smaller amounts of iron. The lunar surface rocks often have higher metal content, but are neglected here.
The structural aluminum considered for use in colony-building is an alloy of aluminum and silicon, the most plentiful of lunar elements after oxygen.
The fuel estimate made is based on the usual 6:1 oxygen/ hydrogen mixture (fuel-rich) commonly used for LOX-hydrogen rocket engines.
D. Criswell (ref. 5) has calculated the yields of carbon nitrogen and hydrogen which could be obtained by sifting lunar soils for the finegrained material, and then heating that material. The rare light elements are concentrated in the finer grains, and can be extracted by that process. In this report no advantage is taken of that option.
Asteroidal materials: As noted earlier, the velocity interval from the earth to L5 is about 11.4 Km/sec. A selection of ten asteroids, whose orbital elements are well-known, was checked. It was found that in all cases the total velocity interval required for transfer to L5 was close to 10 Km/sec. Correction to match the orbital plane with that of the earth was an important term.
The design of Figures 10 and 11 has a habitat-intenor diameter of 540 meters and a circumference of 1.05 miles. Total interior non-window surface area is over 900,000 me, about half of which is at 70% or more of earth gravity. The counter-rotating toroidal agriculture ring provides 400,000 to one million m2 for photosynthetic crop-growing, plus additional covered areas for processing and storage.
In order that the entire colony maintain its axis always pointed toward the sun yet not require thrusters, the total rotational angular momentum must be zero. In the "Sunflower" design this is accomplished by devoting about 20% of the total mass to the agricultural ring.
The low-gravity work areas described are nominally 40 meters in diameter (412 ft. circumference or floor width) and can be of any desired length. Six of them, each 200 meters long, would provide approximately three times the total high-bay assembly area of the General Electric Large Turbine Division plant at Schenectady, New York, where a large fraction of the turbogenerator capacity of the USA is built.
Atmospheric composition: A typical design for a hemisphere diameter of 540 meters has the following contributions to total internal pressure:
|Aluminum weight||3.2cm||0.13 psi|
|Soil or structures |
|30 cm||1.08 psi|
In this typical case the atmospheric pressure accounts for 86% of the total structural requirement. With a full 14.7 psi of atmospheric pressure the figure would be 92%.
In Table 2, items (a) and (c) are from the Exxon Corporation (Smithsonian Magazine, April 1975, p. 117).
Item (e) assumes a cost of 23 Billion Dollars as of 1967 and an average of 7% inflation since that year.
Item (f) is based on an unpublished NASA/MSFC Study Document, "Space Colonization by the Year 2000 - An Assessment. "
Item (g) is from J.N. Wilford, New York Times, July 13 1975, quoting Vance Brand, U.S. Astronaut.
Value added by location in high orbit: A fully employed population, a productivity of 20 tons/person-year, and lift costs in the range $100 - $400 per pound are assumed.
Busbar power costs: Present figures average 15 mils/Kwh for nuclear power, 17 mils/Kwh for fossil-fuel power. Peak shaving power earns revenue at a much higher rate, but the energy generated by peak-shaving generators is a small fraction of the total.
Solar energy arriving on the land area of the continental U.S. averages about 1/10 of the amount which intercepts equal area in free space. For base-load power, the capital cost of the system must provide for a December/January day length, storage for extended bad weather, and a high demand.
Fifty-four percent efficiency has been demonstrated in 1975 by a JPL group, in cooperation with Raytheon (also Cf. ref.8 ).
Microwave power transmission has its own environmental problems, but they appear to be less serious than those of nuclear or fossil-fuel power (Cf.refs.8 and 9 ).
The velocity interval from L5 to geosynchronous (spiral orbit transfer) is 1.1 Km/sec and is in full sunshine. Transfer could be by a mass-driver, powered by the SSPS itself and used as a reaction engine. The reaction mass could be the wastes (for example liquid oxygen) from the industrial processing at L5. A transfer time of one month or less appears feasible.
Vehicle development costs: for an advanced (non-shuttle-derived) heavy lift vehicle, estimates of development cost from within the aerospace industry vary from 5 billion dollars to 25 billion dollars; of attainable launch costs to geosynchronous, from $77/Kg to $400/Kg.
The costs of SSPS construction at L5 (input for Figures 14, 15 and 16) include lift costs for microwave transmitter magnets and initially for computers and controls, as well as items listed in the text.
Alaskan oil field comparison: 1 barrel of oil has an energy content of 5.24 x 109 joules (ref. 10). The peak capacity of the Alaska pipeline will be 2 x 106 barrels/day (ref. 11). For a high conversion efficiency of 48%, the pipeline wilI then supply 1.83 x 1018 joules annually. This is a rate of 5.8 x 1010 watts, or 58,000 megawatts, equivalent to less than 125,000 megawatt SSPS units.
The estimated total reservoir of oil in the Alaskan North Slope (the pipeline source) is 1010 barrels (ref. 11), or 2.1 x 1019 joules at 48% conversion efficiency. This is 134 SSPS-years, a total reached in the first nine years with the growth rates assumed for Figures 14 - 16. For comparison, the total proven reserve of oil in the Middle East is 33.8 x 1010 barrels (ref. 12 ).
One area requiring verification is semi-closed-cycle ecology. Many small islands have effective ecosystems more limited than that of the first colony, but verification is still required. Fortunately, total closure is unnecessary: "economic closure," the achievement of a closure level adequate to reduce to tolerable levels the lift costs for seeds, etc. from the earth, will be sufficient. Isolation and heat-sterilization can halt any runaway biological subsystem.
IS THE SURFACE OF A PLANET REALLY THE RIGHT PLACE FOR AN EXPANDING TECHNOLOGICAL CIVILIZATION?
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